Abstract

The observed relationship between magnitude and duration is shown to be a result of the particular shape of the signal coda as a function of time. If the envelope of the coda follows a t−q relationship with increasing time, then the magnitude, mτ, based on a duration τ is consequently of the form

 
mτ=qlog10τ+r.

A study of the duration-magnitude and duration-moment relationships for a set of central United States earthquakes indicates that the linear relationship between mτ and log10τ is valid only over a limited range. The departure from the simple linear dependence is explained in terms of instrumental response and the shift of the source-spectrum corner frequency with increasing event size.

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